McAfee [1]} takes a different approach. Instead of struggling with the hard task of explicitly computing the second-best mechanism, McAfee suggests the Median mechanism: let \(p\)  be the median of the seller distribution \({\mathcal {F}^H_s}\) . Trade occurs if and only if \(b\ge p \ge s\) . McAfee shows that the median mechanism guarantees in expectation at least half of the optimal GFT, but only under the constraint that the median of \({\mathcal {F}^H_s}\)  is at most the median of \({\mathcal {F}^H_b}\) . Blumrosen and Dobzinski [2]} prove that in a sense this constraint is necessary, since there exists a pair of distributions for which no distribution-dependent price can guarantee a constant fraction of the optimal GFT.
